From 80f1ac88befc8c0471a47f4400dd727cbd47eff4 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Tue, 26 Jul 2022 15:14:53 +0200 Subject: Ordner sturuktur angepasst --- buch/papers/fm/FM presentation/A2-14.pdf | Bin 259673 -> 0 bytes buch/papers/fm/FM presentation/FM_presentation.tex | 125 +++++++++++++++++++++ ...quency modulation (FM) and Bessel functions.pdf | Bin 159598 -> 0 bytes buch/papers/fm/FM presentation/README.txt | 1 + ...l2022_Book_H\303\266hereMathematikImAlltag.pdf" | Bin 4118379 -> 0 bytes buch/papers/fm/FM presentation/images/100HZ.png | Bin 0 -> 8601 bytes buch/papers/fm/FM presentation/images/200HZ.png | Bin 0 -> 8502 bytes buch/papers/fm/FM presentation/images/300HZ.png | Bin 0 -> 9059 bytes buch/papers/fm/FM presentation/images/400HZ.png | Bin 0 -> 9949 bytes buch/papers/fm/FM presentation/images/bessel.png | Bin 0 -> 40393 bytes buch/papers/fm/FM presentation/images/bessel2.png | Bin 0 -> 102494 bytes .../fm/FM presentation/images/bessel_beta1.png | Bin 0 -> 40696 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buch/papers/fm/FM presentation/images/fm_7Hz.png create mode 100644 buch/papers/fm/FM presentation/images/fm_frequenz.png create mode 100644 buch/papers/fm/FM presentation/images/fm_in_time.png (limited to 'buch/papers/fm/FM presentation') diff --git a/buch/papers/fm/FM presentation/A2-14.pdf b/buch/papers/fm/FM presentation/A2-14.pdf deleted file mode 100644 index 7348cca..0000000 Binary files a/buch/papers/fm/FM presentation/A2-14.pdf and /dev/null differ diff --git a/buch/papers/fm/FM presentation/FM_presentation.tex b/buch/papers/fm/FM presentation/FM_presentation.tex new file mode 100644 index 0000000..2801e69 --- /dev/null +++ b/buch/papers/fm/FM presentation/FM_presentation.tex @@ -0,0 +1,125 @@ +%% !TeX root = .tex + +\documentclass[11pt,aspectratio=169]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{lmodern} +\usepackage[ngerman]{babel} +\usepackage{tikz} +\usetheme{Hannover} + +\begin{document} + \author{Joshua Bär} + \title{FM - Bessel} + \subtitle{} + \logo{} + \institute{OST Ostschweizer Fachhochschule} + \date{16.5.2022} + \subject{Mathematisches Seminar - Spezielle Funktionen} + %\setbeamercovered{transparent} + \setbeamercovered{invisible} + \setbeamertemplate{navigation symbols}{} + \begin{frame}[plain] + \maketitle + \end{frame} +%------------------------------------------------------------------------------- +\section{Einführung} + \begin{frame} + \frametitle{Frequenzmodulation} + + \visible<1->{ + \begin{equation} \cos(\omega_c t+\beta\sin(\omega_mt)) + \end{equation}} + + \only<2>{\includegraphics[scale= 0.7]{images/fm_in_time.png}} + \only<3>{\includegraphics[scale= 0.7]{images/fm_frequenz.png}} + \only<4>{\includegraphics[scale= 0.7]{images/bessel_frequenz.png}} + + + \end{frame} +%------------------------------------------------------------------------------- +\section{Proof} +\begin{frame} + \frametitle{Bessel} + + \visible<1->{\begin{align} + \cos(\beta\sin\varphi) + &= + J_0(\beta) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) + \\ + \sin(\beta\sin\varphi) + &= + J_0(\beta) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) + \\ + J_{-n}(\beta) &= (-1)^n J_n(\beta) + \end{align}} + \visible<2->{\begin{align} + \cos(A + B) + &= + \cos(A)\cos(B)-\sin(A)\sin(B) + \\ + 2\cos (A)\cos (B) + &= + \cos(A-B)+\cos(A+B) + \\ + 2\sin(A)\sin(B) + &= + \cos(A-B)-\cos(A+B) + \end{align}} +\end{frame} + +%------------------------------------------------------------------------------- +\begin{frame} + \frametitle{Prof->Done} + \begin{align} + \cos(\omega_ct+\beta\sin(\omega_mt)) + &= + \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t) + \end{align} + \end{frame} +%------------------------------------------------------------------------------- + \begin{frame} + \begin{figure} + \only<1>{\includegraphics[scale = 0.75]{images/fm_frequenz.png}} + \only<2>{\includegraphics[scale = 0.75]{images/bessel_frequenz.png}} + \end{figure} + \end{frame} +%------------------------------------------------------------------------------- +\section{Input Parameter} + \begin{frame} + \frametitle{Träger-Frequenz Parameter} + \onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} + \only<1>{\includegraphics[scale=0.75]{images/100HZ.png}} + \only<2>{\includegraphics[scale=0.75]{images/200HZ.png}} + \only<3>{\includegraphics[scale=0.75]{images/300HZ.png}} + \only<4>{\includegraphics[scale=0.75]{images/400HZ.png}} + \end{frame} +%------------------------------------------------------------------------------- +\begin{frame} +\frametitle{Modulations-Frequenz Parameter} +\onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} +\only<1>{\includegraphics[scale=0.75]{images/fm_3Hz.png}} +\only<2>{\includegraphics[scale=0.75]{images/fm_5Hz.png}} +\only<3>{\includegraphics[scale=0.75]{images/fm_7Hz.png}} +\only<4>{\includegraphics[scale=0.75]{images/fm_10Hz.png}} +\only<5>{\includegraphics[scale=0.75]{images/fm_20Hz.png}} +\only<6>{\includegraphics[scale=0.75]{images/fm_30Hz.png}} +\end{frame} +%------------------------------------------------------------------------------- +\begin{frame} +\frametitle{Beta Parameter} + \onslide<1->{\begin{equation}\sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t)\end{equation}} + \only<1>{\includegraphics[scale=0.7]{images/beta_0.001.png}} + \only<2>{\includegraphics[scale=0.7]{images/beta_0.1.png}} + \only<3>{\includegraphics[scale=0.7]{images/beta_0.5.png}} + \only<4>{\includegraphics[scale=0.7]{images/beta_1.png}} + \only<5>{\includegraphics[scale=0.7]{images/beta_2.png}} + \only<6>{\includegraphics[scale=0.7]{images/beta_3.png}} + \only<7>{\includegraphics[scale=0.7]{images/bessel.png}} +\end{frame} +%------------------------------------------------------------------------------- +\begin{frame} + \includegraphics[scale=0.5]{images/beta_1.png} + \includegraphics[scale=0.5]{images/bessel.png} +\end{frame} +\end{document} diff --git a/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf b/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf deleted file mode 100644 index a6e701c..0000000 Binary files a/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf and /dev/null differ diff --git a/buch/papers/fm/FM presentation/README.txt b/buch/papers/fm/FM presentation/README.txt new file mode 100644 index 0000000..65f390d --- /dev/null +++ b/buch/papers/fm/FM presentation/README.txt @@ -0,0 +1 @@ +Dies ist die Presentation des FM - Bessel \ No newline at end of file diff --git "a/buch/papers/fm/FM presentation/Seydel2022_Book_H\303\266hereMathematikImAlltag.pdf" "b/buch/papers/fm/FM presentation/Seydel2022_Book_H\303\266hereMathematikImAlltag.pdf" deleted file mode 100644 index 2a0bddd..0000000 Binary files "a/buch/papers/fm/FM presentation/Seydel2022_Book_H\303\266hereMathematikImAlltag.pdf" and 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